The SSL certificate (for https) is assigned to a different website when it should be assigned to us. This means our site is not secure when it should be. We need to secure it by making LetsEncrypt aware of this, but they ‘do not offer support over email,’ so here we are. Any help would be appreciated.

Our name isn’t the ‘Common name’ at all, and it’s that that seems to be causing the problem. The certificate is registered as belonging to our domain but in reality applies to someone else. Our web host is GoDaddy: is it 100% up to them to fix it?

An American visitor to the site learned that its certificate was faulty and unsecured

Please please please give some specific detail as to what is wrong/insecure/faulty.
Was there an “alert”, a “popup”, a “failed connection”, …

The only thing I can “find” that might be causing some (significantly older systems) trouble:
Is that the default certificate associated with the IP does not include your site.
That is, if a device connects to your site but is unable to manage the connection via FQDN and reverts to IP it will fail to find your site.

All I know is that the https isn’t working. An American visitor to the site found its certificate was wrong. I thought it was to do with the common name difference, but if it’s not I have no idea what’s causing it.

EDIT: They had a pop-up. It was a pop-up that said the security certificate needed updating, with a yellow triangle exclamation mark icon.

Perhaps the certificate was expired and it was then renewed by your system administrator?

On what date did you receive the report of the problem?

I’d be inclined to disregard that report unless you have a way to reproduce the problem. Sometimes there are problems that are local to the visitor (such as their system clock being wrong or other types of computer issues) which can manifest in such error screens.

There was likely no expiry, as it is due to expire in 40 days anyway. First I learned of this was a month ago. It seems it was local issue; l will try to confirm by asking other foreign users and, if not, return to this topic. Thank you all for your help!